Fungrim entry: e4315f

\left\{ \lambda(\tau) : \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, \left|\tau + \frac{1}{2}\right| = \frac{1}{2} \right\} = \left(1, \infty\right)

This mapping is one-to-one.

References:

J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987. p. 118.

TeX:

\left\{ \lambda(\tau) : \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, \left|\tau + \frac{1}{2}\right| = \frac{1}{2} \right\} = \left(1, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`HH`	$\mathbb{H}$	Upper complex half-plane
`Abs`	$\left\|z\right\|$	Absolute value
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("e4315f"),
    Formula(Equal(Set(ModularLambda(tau), ForElement(tau, HH), Equal(Abs(Add(tau, Div(1, 2))), Div(1, 2))), OpenInterval(1, Infinity))),
    Description("This mapping is one-to-one."),
    References("J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987. p. 118."))

Topics using this entry

Modular lambda function